Question

а The probability of finding an elephant in a national park is 0.7, the probability of finding a cheetah is 0.4, and the probability of finding an elephant or Cheetah or both is 0.8. What is the probability that; (a) Both animals will be spotted? (b) Neither of the animals will be spotted?

Answer 1

Given:

The probability of finding an elephant in a national park is 0.7.

The probability of finding a cheetah in a national park is 0.4.

The probability of finding an elephant or Cheetah or both is 0.8.

`\begin{gathered} P(E)=0.7 \\ P(C)=0.4 \\ P(E\text{ or C or both)=0.8} \end{gathered}`

a) The probability that both the animals will be spotted is,

`\begin{gathered} P(E\text{ or C)=P(E)+P(C)-P(E and C)} \\ 0.8=0.7+0.4-\text{P(E and C)} \\ \text{P(E and C)}=0.3 \end{gathered}`

b) The probability of Neither of the animal will be spotted is,

`P(\text{not (E and C))=1-P(E and C)=1-0.3=0.7}`

Answer:

a) probability is 0.3.

b) probability is 0.7.