Question

probability that A passes a test is 2/3 and B is 3/5. What is probability only one of them passes

Answer 1

Answer:

The required answer is $7/15$.

Step-by-step explanation:

P(B) = $3/5$; P(NOT B) = $2/5$

P(A) = $2/3$; P(NOT A) =$1/3$

Probabilities for every scenario:

P(A AND B) = $2/3*3/5$ = $6/15$ (un simplified) A and B pass.

P(A AND NOT B) = $\frac{2}{3} * \frac{2}{5}$ = $4/15$ (un simplified) Only A passes.

P(NOT A AND B) = $1/3 * 3/5 = 3/15$; Only B passes

P(NOT A AND NOT B) = $2/5 * 1/3 = 2/15$; Neither passes

Note that $6/15 + 4/15 + 3/15 + 2/15 = 15/15=1$

SO, P(either A OR B but not both passing) $= 3/15 +4/15 = 7/15$.

Hence, the probability only one of them passes is $7/15$.

#SPJ3

Answer 2

Answer: Probability that only one of A and B pass is 7/15

Step-by-step explanation:

Cases when only one student pass :

• A passes and  B fails
• A fails and B passes

Probability of A passing = $\frac{2}{3}$

Probability of A failing = 1 - Probability of A passing = $1 - \frac{2}{3}$  =  $\frac{1}{3}$

Probability of B passing = $\frac{3}{5}$

Probability of B failing = 1 - Probability of B passing = $1 - \frac{3}{5}$  =  $\frac{2}{5}$

Probability of A passing and B failing =  $\frac{2}{3}$ ×   $\frac{2}{5}$  =  $\frac{4}{15}$

Probability of A falling and B passing =  $\frac{1}{3}$ ×   $\frac{3}{5}$  =  $\frac{3}{15}$

Net probability of only one student passing = $\frac{4}{15} + \frac{3}{15} = \frac{7}{15}$

#SPJ1