Вероятност

[Гост]

Здравейте,
Бихте ли ми помогнали със следната задачка:

Тест за Ковид 19 дава положителен резултат при заразен човек с вероятност 0.9 и отрицателен резултат при незаразен човек с верятност 0.8. Каква е вероятността човек да е заразен, ако два последователни теста са дали отрицателен резултат

[pal702004]

Заразен е с вероятност $\dfrac{1}{65}\approx 0.01538$ и не е заразен с вероятност $\dfrac{64}{65} \approx 0.98462$

[Гост]

Заразен е с вероятност <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>1</mn><mn>65</mn></mfrac><mo>≈</mo><mn>0.01538</mn></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \dfrac{1}{65}\approx 0.01538</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 2.00744em; vertical-align: -0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.32144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">6</span><span class="mord">5</span></span></span><span class="" style="top: -3.22em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.06em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.686em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 0.64444em; vertical-align: 0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">0</span><span class="mord">1</span><span class="mord">5</span><span class="mord">3</span><span class="mord">8</span></span></span></span></span> и не е заразен с вероятност <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>64</mn><mn>65</mn></mfrac><mo>≈</mo><mn>0.98462</mn></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \dfrac{64}{65} \approx 0.98462</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 2.00744em; vertical-align: -0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.32144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">6</span><span class="mord">5</span></span></span><span class="" style="top: -3.22em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.06em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">6</span><span class="mord">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.686em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 0.64444em; vertical-align: 0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">9</span><span class="mord">8</span><span class="mord">4</span><span class="mord">6</span><span class="mord">2</span></span></span></span></span>

Може ли да ми подскажете, коя фомула изполвахте и как стигнахте до този отговор ?

[Гост]

Заразен е с вероятност <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>1</mn><mn>65</mn></mfrac><mo>≈</mo><mn>0.01538</mn></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \dfrac{1}{65}\approx 0.01538</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 2.00744em; vertical-align: -0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.32144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">6</span><span class="mord">5</span></span></span><span class="" style="top: -3.2199999999999998em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.06em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.686em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right: 0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height: 0.64444em; vertical-align: 0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">0</span><span class="mord">1</span><span class="mord">5</span><span class="mord">3</span><span class="mord">8</span></span></span></span></span> и не е заразен с вероятност <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>64</mn><mn>65</mn></mfrac><mo>≈</mo><mn>0.98462</mn></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \dfrac{64}{65} \approx 0.98462</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 2.00744em; vertical-align: -0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.32144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">6</span><span class="mord">5</span></span></span><span class="" style="top: -3.2199999999999998em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.06em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord">6</span><span class="mord">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.686em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right: 0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height: 0.64444em; vertical-align: 0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">9</span><span class="mord">8</span><span class="mord">4</span><span class="mord">6</span><span class="mord">2</span></span></span></span></span>

[Гост]

Заразен е с вероятност $\dfrac{1}{65}\approx 0.01538$ и не е заразен с вероятност $\dfrac{64}{65} \approx 0.98462$

Здравейте,
Може ли малко разяснение как се стига до отговора?