Question

Weather Forecast In the month of May, the weather forecast department gives the prediction of weather for the month of June. The given table shows the probabilities of forecast of different days: Sunny Partially doudy Days Sunny Cloudy Rainy Partially cloudy 1 1 Probability Y 2 5 Cloudy Rainy If the forecast is 100% correct for lune, then answer the following questions If the sum of x and y is 3 10 then the number of rainy days in June is, 1 2 ال) G) Q o​

Answer 1

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Answer 2

Number of sunny days in June is 15 so option c) is correct.

If the number of cloudy days in June is 5 then x is $\frac{1}{6}$ so option b) is correct.

The probability that the day is not rainy is $\frac{13}{15}$ so option a) is correct

The number of rainy days in June is 4 so option d) is correct.

The number of rainy days in June is 6 so option c) is correct.

Given : Weather Forecast In the month of May, the weather forecast department gives the prediction of weather for the month of June. The table shows the probabilities of forecast of different days:

To Find :

i ) The number of sunny days in June

a) 5   b) 10  c) 15  d) 20

ii ) If the number of cloudy days in June is 5 then x is

a) $\frac{1}{4}$    b)  $\frac{1}{6}$   c)  $\frac{1}{8}$     d) $\frac{1}{10}$

iii) The probability that the day is not rainy is

a) $\frac{13}{15}$  b) $\frac{11}{15}$  c) $\frac{1}{15}$  d) None of these

iv) If the sum of x and y is $\frac{3}{10}$ then the number of rainy days in June is

a) 1   b) 2   c) 3   d) 4

v)  Find the number of partially cloudy days

a) 2   b) 4   c) 6  d) 8

Solution :

i) Number of sunny days in June is 15 so option c) is correct.

Since the probability of sunny days in June is $\frac{1}{2}$ and total number of days in June is 30

So number of sunny days in June is $\frac{30}{2}$ = 15

ii) If the number of cloudy days in June is 5 then x is $\frac{1}{6}$ so option b) is correct.

Number of cloudy days is 5 (Given)

and total no of days in June is 30

Probability of cloudy day (x) is No of cloudy day / Total no of days in June

so x = $\frac{5}{30}$ = $\frac{1}{6}$

iii) The probability that the day is not rainy is $\frac{13}{15}$ so option a) is correct

Since the probability of sunny day is $\frac{1}{2}$ (Given)

the probability of cloudy day is $\frac{1}{6}$ (From ii))

the probability of partially cloudy day is  $\frac{1}{5}$  (Given)

the probability of rainy day is y  (Given)

The sum of all these probabilities is 1

So $\frac{1}{2} +\frac{1}{6} +\frac{1}{5} + y = 1$

$\frac{26}{30}+y = 1$

$y = 1- \frac{26}{30}$

$y = \frac{2}{15}$

probability of rainy day is $\frac{2}{15}$ so probability of not rainy day is $1-\frac{2}{15}$

= $\frac{13}{15}$

iv) The number of rainy days in June is 4 so option d) is correct.

Probability of rainy day is $\frac{2}{15}$ (from iii))

So number of rainy day in June is $\frac{2}{15}$ × 30

= 4 days

v) The number of rainy days in June is 6 so option c) is correct.

the probability of partially cloudy day is  $\frac{1}{5}$  (Given)

Total no of days in June is 30

then total no of  partially cloudy day is  $\frac{1}{5}$ × 30

= 6

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