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Probability · Rajasthan Board (RBSE) STD 11 Science (Rajasthan - English Medium). 5 questions.

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Fill In The Blanks[1 Marks ]

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Question 11 Mark
The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is __________.
Answer
The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is 0.2
Solution:
$\text{P}(\bar{\text{A}}\cap\bar{\text{B}})=\text{P}(\overline{\text{A}\cup\text{B}})$
$=1-\text{P}(\text{A}\cup\text{B})$
$=1-\big[\text{P(A)}+\text{P(B)}\big]$ [Since, A and B are mutually exclusive]
$=1-(0.5+0.3)$
$=1-0.8=0.2$
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Question 21 Mark
If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and $\text{P}(\text{A}\cap\text{B})=0.1,$ then the value of $\text{P}(\text{A}\cap\bar{\text{B}})$ is ____________.
Answer
If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and $\text{P}(\text{A}\cap\text{B})=0.1,$ then the value of $\text{P}(\text{A}\cap\bar{\text{B}})$ is 0.2
Solution:
$\text{P}(\text{A}\cap\bar{\text{B}})=\text{P(A)}-\text{P}(\text{A}\cap\text{B})$
$=0.3-0.1=0.2$
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Question 31 Mark
If e1, e2, e3, e4 are the four elementary outcomes in a sample space and P(e1) = 0.1, P(e2) = 0.5, P (e3) = 0.1, then the probability of e4 is ___________.
Answer
If e1, e2, e3, e4 are the four elementary outcomes in a sample space and P(e1) = 0.1, P(e2) = 0.5, P (e3) = 0.1, then the probability of e4 is 0.3
Solution:
$\text{P}(\text{E}_1)+\text{P}(\text{E}_2)+\text{P}(\text{E}_3)+\text{P}(\text{E}_4)=1$
$\Rightarrow0.1+0.5+0.1+\text{P}(\text{E}_4)=1$
$\Rightarrow0.7+\text{P}(\text{E}_4)=1$
$\therefore\ \text{P}(\text{E}_4)=0.3$
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Question 41 Mark
The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is __________.
Answer
The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is 0.15
Solution:
P(losing) = 1 - (0.77 + 0.08) = 0.15
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Question 51 Mark
Let S = {1, 2, 3, 4, 5, 6} and E = {1, 3, 5}, then $\bar{\text{E}}$is __________.
Answer
Let S = {1, 2, 3, 4, 5, 6} and E = {1, 3, 5}, then $\bar{\text{E}}$is {2, 4, 6}.
Solution:
Here, S = {1, 2, 3, 4, 5, 6}
and E = {1, 3, 5}
$\therefore\ \bar{\text{E}}=\text{S}-\text{E}=\{2,4,6\}$
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