Theory of Probability I
In this chapter we will discuss about some basic and important MCQs on Probability for competitive exam purpose. Before you try to solve the questions, you should have compact idea of coin tossing, card play, different events like mutually exclusive event, equally likely event etc and other formulas.
1.In a random test of a unbiased coin, head and tail are ______________________ event.
- Mutually exclusive
- Independent
- Equally likely
- None
Ans: Equally likely
2.Two unbiased dices are thrown, then what is the probability that both dice will show the same number?
- 1/6
- 1/18
- 1/12
- 5/36
3.From 25 tickets, marked with 1 to 25, one is drawn at random. Find the chance that it will be multiple of 5 or 7?
- 10/25
- 8/25
- 9/25
- 4/25
4.Four cards are drawn at random from the pack of 52 cards . What is the probability of having two kings and two queens?
- $\frac{\binom{4}{2}\times \binom{4}{2}}{\binom{52}{4}}$
- $\frac{\binom{4}{2}}{\binom{52}{4}}$
- $\frac{\binom{4}{2}\times \binom{4}{2}}{\binom{52}{2}}$
5.An urn contains 6 white balls,4 red balls, 9 black balls.If 3 balls are drawn at random what will the probability of getting two white balls?
- $\frac{\binom{6}{2}\times \binom{13}{1}}{\binom{19}{3}}$
- $\frac{\binom{6}{1}\times \binom{13}{2}}{\binom{19}{3}}$
- $\frac{\binom{6}{3}}{\binom{19}{3}}$
6.$.P(A\cap B)$= $P(A)P(B)$ is valid for
- independent variable
- dependent variable
- none
7.Find the expression in the context of A,B and C for "at least one occurs"
- $A\cup B\cup C$
- $A\cap B\cap C$
- $A\cap B\cup C$
8. An investment company predicts that the odds against the price of a certain stock will go up during the next week are 2:1. The odds in favour of the price remaining the same are 1:3. What is the probability that the price of the stock will go down during the next week?
- 5/12
- 7/12
- 4/12
- 3/12
9. If the conditional probability of A given B is $\frac{3}{4}$ , and the $P(A \cap B)$ = $\frac{3}{16}$ , then what is the value of P(B)=?
- $\frac{1}{4}$
- $\frac{2}{4}$
- $\frac{3}{16}$
- None
10.A problem can be solve by A,B,C with the probability of 1/2,3/4,1/4 respectively. Then what is the probability that the problem will be solved by all of them independently?
- 29/32
- 64/128
- 9/32
- 10/64
11.A speaks truth 4 out of 5 times. A die is tossed. He reports that there is a six. What is the chance that there is actually a six?
- 4/9
- 3/9
- 1/9
- 2/8
Ans: 4/9
Do your self:
1.What is the probability of draw3ing a spade from a pack of cards?
2.A coin is tossed three times in succession, the number of sample points in sample space is_______________.
3.What is the probability that the letter will be vowel, if you select a a single letter form "Probability"?
4.A urn contains 9 balls, two of which are red, three blue and four black. Three balls are drawn at random. What is the chance that they are of the same color?
5. $P(A\cap B)$=1/2, $P(\bar A \cap \bar B)$=1/2 and $2P(A)=P(B)=p$ then what will be the value the p?
6.A and B are two independent events such that $P(\bar A)$ =0.7, $P(\bar B)$=k and $P(A \cup B)$ =0.8, then the value of the k is _________________.
7.Two events S and T are independent whit $P(S)<P(T$), $P(S \cap T)$ =6/25, ans $P(S|T) + P(T|S)$ =1. Then $P(S)$ =?
8. Two cards drawn at random from a well shuffled pack of 52 cards. Show that the chances of drawing two aces is 1/221.
9.If $P(A \cup B)$=5/6, $P(A \cap B)$=1/3, and $P(\bar A)$ =1/2, find $P(A)$ and $P(B)$?
10.Two six faced unbiased dice are thrown. Find the probability that the sum of the numbers shown is 7 or product is 12.
11.From a vessel containing 3 white and 5 black balls, 4 balls are transferred into an empty vessel. From this vessel a ball is drawn and found to be white. What is the probability that out of four balls transferred 3 are white and 1 is black?
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