Probability Test

Result

Probability Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Mean number of ' sixes' in four throws of a fair dice is

A

B

C
1

D
Question 2
1 / -0

A coin is tossed once. If a head comes up , then it is tossed again and if a tail comes up , a dice is thrown . The number of points in the sample space of experiment is

A
24

B
8

C
12

D
4

Solution

Sample Space is
S = { HH, HT, T1, T2, T3, T4, T5, T6 }
so number of outcomes in sample space is 8
Question 3
1 / -0

Five letters are sent to different persons and addresses on the five envelopes are written at random. The probability that all the letters reach the correct destiny is

A

B

C

D
None of these
Question 4
1 / -0

A coin with tail on both sides is tossed twice. The probability of getting ' a head' is

A

B
1

C
0

D
Question 5
1 / -0

The probability of the having atleast one tail in 4 tosses with a coin is

A

B

C

D
1
Question 6
1 / -0

A digit is selected at random from either of two sets {1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. What is the chance that the sum of the digits selected is 10?

A

B

C

D
None of these
Question 7
1 / -0

A cubical dice has 3 on three faces, 2 on two faces and 1 on the 6th face .It is tossed twice. The chance that both the tosses show an even number is

A
1/ 9

B
1/ 36

C
5/36

D
1/ 4

Solution

Let X denote getting an even number on each dice on throwing twice.
By only one way it can be done by having 2 in both dice.
Since 2 occupy two faces of dice.
So P(getting 2 in 1st dice) = 2/6
Also P ( getting 2 in 2nd dice) = 2/6
So P ( getting 2 in both dice dice) = 2/6 × 2/6 = 1/9 [from multiplication theorem of probabilty P(A ∩ B) = P(A)xP(B) for any two non empty sets A, B]
Question 8
1 / -0

Three fair dice are tossed once. The probability that they show the same numbers is

A
1/ 12

B
1/ 18

C
1/ 36

D
7/ 36

Solution

When three dice are rolled, total number of outcomes =n(S)=n=63 =216
It is given that the numbers on all the three dice are identical
Hence the favourable outcomes are (1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6)
Hence no. of favourable outcomes=m=6
Hence required probability=mn=6/216=1/36
Question 9
1 / -0

Probability of getting a number between 1 and 100, which is divisible by 1 and itself only, is

A
1/ 4

B
25/ 98

C
25/ 99

D
none of these

Solution

the numbers which are divisible by 1 and itself are prime numbers
Prime numbers between 1 and 100 are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 . Total prime numbers 25 out of 98 numbers .
P(Getting a number divisible by 1 and itself )=favourable out come/total no.of out comes =25/98
Question 10
1 / -0

Probability of getting a number between 1 and 100, which is divisible by 1 and itself only, is

A
1/ 4

B
25/ 98

C
25/ 99

D
none of these

Solution

the numbers which are divisible by 1 and itself are prime numbers
Prime numbers between 1 and 100 are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 . Total prime numbers 25 out of 98 numbers .
P(Getting a number divisible by 1 and itself )=favourable out come/total no.of out comes =25/98
Question 11
1 / -0

The chance that an event E ' occurs' or ' does not occur' is

A
0

B
1

C
2

D
None of these
Question 12
1 / -0

A coin is tossed 6 times. The probability of getting a head three times is

A

B

C

D
Question 13
1 / -0

From a deck of 52 cards, the probability of drawing a court card is

A

B

C

D
Question 14
1 / -0

Three letters are written to different persons and addresses on the envelopes are also written. Without looking at the addresses, the letters are put into the envelopes. The probability that the letters go into right envelopes is

A

B

C

D
Question 15
1 / -0

From each of the four married couples, one of the parteners is selected at random. The probability that those selected are of the same sex is

A

B

C

D