a recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back…

a recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back and front pockets. suppose a pair of jeans is selected at random and it is determined that it has front pockets. what is the probability that a randomly selected pair of jeans with front pockets also has back pockets?\n0.52\n0.60\n0.74\n0.81

a recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back and front pockets. suppose a pair of jeans is selected at random and it is determined that it has front pockets. what is the probability that a randomly selected pair of jeans with front pockets also has back pockets?\n0.52\n0.60\n0.74\n0.81

Answer

Explanation:

Step1: Define events

Let $A$ be the event that jeans have back - pockets, $P(A)=0.8$; let $B$ be the event that jeans have front - pockets, $P(B)=0.65$; and $P(A\cap B)=0.48$.

Step2: Use conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$.

Step3: Substitute values

Substitute $P(A\cap B) = 0.48$ and $P(B)=0.65$ into the formula: $P(A|B)=\frac{0.48}{0.65}\approx0.74$.

Answer:

0.74