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Standard IX

Mathematics

Experimental/Empirical Probability

If A and ...

Question

If $A$ and $B$ are two events associated with a random experiment such that $P (B) = 0.35, P (A o r B) = 0.85$ and $P (A a n d B) = 0.15$ , find $P (A)$ .

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Solution

P(A or B) = P(A) + P(B) - P(A and B)
0.85 = P(A) + 0.35 - 0.15
P(A) = 0.65

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Similar questions

Q. If A and B are two events associated with a random experiment for which

P (A) = 0.35, P (A or B) = 0.85, and P(A and B) = 0.15.

Find P(only B).

Q. If A and B are two events associated with a random experiment such that
P(A) = 0.5, P(B) = 0.3 and P (A ∩ B) = 0.2, find P (A ∪ B).

Q. (a) If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find:
(i) P (A ∪ B)
(ii)

P (A \cap B)

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∩ B)
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(b) A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35.
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(c) Fill in the blanks in the following table:

	P (A)	P (B)	P (A ∩ B)	P (A ∪ B)
(i)	$\frac{1}{3}$	$\frac{1}{5}$	$\frac{1}{15}$	......
(ii)	0.35	....	0.25	0.6
(iii)	0.5	0.35	.....	0.7

Q. Given two independent events A and B such that P(A)=0.3, P(B)=0.6, Find .

P (A a n d B)

P (A a n d n o t B)

P (A o r B)

P (n e i t h e r A n o r B)

(a) If A and B be mutualy exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find :
(i) $P (A \cup B)$ (ii) $P (¯ ¯¯ ¯ A \cup ¯ ¯¯ ¯ B)$

(iii) $P (¯ ¯¯ ¯ A \cup B)$ (iv) $P (A \cup ¯ ¯¯ ¯ B)$

(b) A and B are two events such that P(A)= 0.54, P(B) = 0.69 and $P (A \cup B)$ = 0.35. Find:

(i) $P (A \cup B)$ (ii) $P (¯ ¯¯ ¯ A \cup ¯ ¯¯ ¯ B)$

(iii) $P (A \cup ¯ ¯¯ ¯ B)$ (iv) $P (B \cup ¯ ¯¯ ¯ A)$

P(A) P(B)

$P (A \cap B)$ $P (A \cup B)$

(i) $\frac{1}{3}$ $\frac{1}{5}$ $\frac{1}{15}$ ___

(ii) 0.35 ___ 0.25 0.6

(iii) 0.5 0.35 ___ 0.7

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If A and B are two events associated with a random experiment such that P(B)=0.35,P(A or B)=0.85 and P(A and B)=0.15, find P(A).

P(A or B) = P(A) + P(B) - P(A and B)0.85 = P(A) + 0.35 - 0.15P(A) = 0.65

If $A$ and $B$ are two events associated with a random experiment such that $P (B) = 0.35, P (A o r B) = 0.85$ and $P (A a n d B) = 0.15$ , find $P (A)$ .

P(A or B) = P(A) + P(B) - P(A and B)
0.85 = P(A) + 0.35 - 0.15
P(A) = 0.65