Question

On a certain day the probability of rain is 80% probability of thunder is 3/5 and the probability of both is 2/5. What is the probability that it will rain or thunder?

Answer 1

Answer:

The probability it will rain or thunder = 100%

Explanation:

Probability it will rain = 80%

P(rain) = 4/5 (simplest term in fraction)

Probability of thunder = 3/5

P(thunder) = 3/5

Probability of both rain and thunder = 2/5

P(rain and thunder) = 2/5

We need to find the probability of rain or thinder = P(rain or thunder)

To find the probability of P(rain or thunder), we will apply the formula for the addition rule on any two events:

$P(A\text{ or B\rparen = P\lparen A\rparen +}P(B)\text{ - P\lparen A and B\rparen}$

Applying the formula in our question:

$P(rain\text{ or thunder\rparen = P\lparen rain\rparen + P\lparen thunder\rparen - P\lparen rain and thunder\rparen}$

substitute the values in order to find the probability:

$\begin{gathered} P(rain\text{ or thunder\rparen = }\frac{4}{5}\text{ + }\frac{3}{5}-\text{ }\frac{2}{5} \\ \\ P(rain\text{ or thunder\rparen = }\frac{4\text{ + 3 - 2}}{5} \\ P(rain\text{ or thunder\rparen = }\frac{5}{5} \\ \\ P(rain\text{ or thunder\rparen = 1} \end{gathered}$

In percentage, the probability it will rain or thunder = 100%