Solveeit Logo
Login

Question

Question: The probability of a boy student getting a scholarship is 0.90 and that of a girl student getting a ...

The probability of a boy student getting a scholarship is 0.90 and that of a girl student getting a scholarship is 0.800.80. The probability that none getting any scholarship is:
A.98100\dfrac{{98}}{{100}}
B.2100\dfrac{2}{{100}}
C.72100\dfrac{{72}}{{100}}
D.28100\dfrac{{28}}{{100}}

Explanation

Solution

Here in this question we have to find the probability of none getting any scholarship. So firstly we will find the probability of at least one of them getting the scholarship. Then we will subtract this probability from 1 to get the probability that none getting any scholarship

Complete step by step solution:
Let P(B)P(B) be the probability of a boy student getting a scholarship and P(G)P(G) be the probability of a girl student getting a scholarship.
It is given that the probability of a boy student getting a scholarship is 0.900.90. Therefore, we get
⇒P(B)=0.90\Rightarrow P(B) = 0.90
Similarly, it is given that the probability of a girl student getting a scholarship is0.800.80. Therefore, we get
⇒P(G)=0.80\Rightarrow P(G) = 0.80
Now we will find the probability of at least one of them getting the scholarship by using the formula.
Probability of at least one of them getting the scholarship =P(B)+P(G)−P(B)×P(G) = P(B) + P(G) - P(B) \times P(G)
∴\therefore Probability of at least one of them getting the scholarship =0.90+0.80−(0.90×0.80)=1.7−0.72=0.98 = 0.90 + 0.80 - \left( {0.90 \times 0.80} \right) = 1.7 - 0.72 = 0.98
Now we have to subtract the probability of at least one of them getting the scholarship from 1 to get the probability of none getting any scholarship. Therefore, we get
⇒\Rightarrow Probability that none getting any scholarship=1−0.98=0.02 = 1 - 0.98 = 0.02
We can write in the fraction form. So, we get
⇒\Rightarrow Probability that none getting any scholarship =0.02=2100 = 0.02 = \dfrac{2}{{100}}
Hence, 2100\dfrac{2}{{100}}is the probability of none getting any scholarship.
So, option B is the correct option.

Note: Here we have to keep in mind that the probability of occurrence is always less than or equal to one. If the probability of the event is one then that event is known as the true event. We should also note that the sum of the probability of occurrence of an event and sum of the probability of not occurrence of an event is always equal to one. We used the same concept to find our required probability. Probability is the subject which helps us a lot in the prediction of the events. We use this probability concept in our day to day life also like in weather forecasting etc.
P(occurrence of event)+P(not occurrence of event)=1P({\text{occurrence of event}}) + P({\text{not occurrence of event}}) = 1