Question

Timas and Theo each shoots at a target. The probability that the target is hit by Timas and Theo are 0.75 and 0.4 respectively.a) find the probability that both miss the targetb) find the probability that only one of them can hit the target.

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

PART A:

Find the probability that both miss the target:

`\begin{gathered} Let\text{ us represent Timas with A} \\ Let\text{ us represent Theo with B} \\ such\text{ that:} \\ P\text{ }(\text{ A })\text{ = 0. 75 }(\text{ Thomas will hit the target}) \\ P(B)\text{ = 0. 4 }(Theo\text{ will hit the target}) \\ Therefore, \\ P(A^1)\text{ = 1- 0. 75 = 0. 25 }(\text{ Thomas will not hit the target }) \\ P(B^1)\text{ = 1- 0. 4 = 0. 6 }(\text{ Theo will not hit the target}) \end{gathered}`
`\begin{gathered} Probability\text{ that both of them will miss the target =} \\ P\text{ }(\text{ A}^1B^1)\text{ = P}(A^1)\text{ X P }(B^1)\text{ =0. 25 X 0. 6 = 0. 15} \\ P(A^1B^1)\text{ = 0. 15} \end{gathered}`

PART B:

Find the probability that only one of them can hit the target =

`\begin{gathered} P\text{ }(\text{ AB}^1)\text{ + P}(\text{ A}^1B\text{ }) \\ =\text{ }(\text{ 0. 75 X 0. 6 })\text{ + }(\text{ 0. 25 X 0. 4 }) \\ =\text{ 0. 45 + 0. 1} \\ =\text{ 0. 55} \end{gathered}`