Question

Chegg There's a pandemic going on, and there are recommendations out there for wearing face coverings. Suppose that a mask reduces the probability of infection by 95% and a face shield reduces it by 72%. What is the reduction in probability of infection for an individual who wears both a mask and face shield, assuming that the effects are independent

Answer 1

Answer:

The reduction in probability of infection for an individual who wears both a mask and face shield is 68.4%

Step-by-step explanation:

Represent the event of wearing a Mask with M

Represent the event of wearing a face shield with F

$P(M) = 95\%$

$P(F) = 72\%$

Required

$P(M\ and\ F)$

Since both events are independent;

$P(M\ and\ F) = P(M) * P(F)$

Substitute values for P(M) and P(F)

$P(M\ and\ F) = 95\% * 72\%$

Convert both percentages to fraction

$P(M\ and\ F) = \frac{95}{100} * \frac{72}{100}$

$P(M\ and\ F) = \frac{95 * 72}{100 * 100}$

$P(M\ and\ F) = \frac{6840}{10000}$

$P(M\ and\ F) = 0.684$

Convert to Percentage

$P(M\ and\ F) = 68.4\%$