The probability of student A passing an examination is 3/7 and of student b passing is 5/7. Assuming the two events Apasses, B passes, as independent, find the probability of: Only A passing the examination Only one of them passing the examination

Explanation

Given:

`{P}_{1}={P}({A})=frac{3}{7}, {P}_{2}={P}({B})=frac{5}{7}`
`therefore` `{q}_{1}={P}(bar{A})=1 cdot {P}({A})=1-frac{3}{7}=frac{4}{7} `

`{q}_{2}={P}(B)=1 cdot {P}({B})=1-frac{5}{7}=frac{2}{7}`


(i) P( only A passes )`=p_{1} q_{2}=frac{3}{7} times frac{2}{7}=frac{6}{49}`
. P (only B passes )`=q_{1} P_{2}=frac{4}{7} times frac{5}{7}=frac{20}{49}`

(ii) P (only one of them passes)` =p_{1} q_{2}+q_{1} P_{2}=frac{3}{7} times frac{2}{7}+frac{4}{7} times frac{5}{7}=frac{26}{49}.`