Mathematics Assessment Questions for IIT JEE Exam on “Probability – Random Experiments-2”.
1. If n coins are tossed simultaneously what is the total number of outcomes?
a) 2n-2
b) 2n-1
c) 2n
d) 2n+1
Answer: c
Clarification: If n coins are tossed simultaneously total number of possible outcomes are 2n.
For 2 coins, it is 4. For 3 coins it is 8 etc.
2. If four dice are rolled simultaneously then what is the total number of possible outcomes?
a) 6
b) 36
c) 216
d) 1296
Answer: d
Clarification: If four dice are rolled simultaneously then total number of possible outcomes is 64=1296.
3. If two dice are simultaneously rolled then what is probability of getting sum 4?
a) 1/6
b) 1/4
c) 1/12
d) 1/9
Answer: c
Clarification: If two dice are simultaneously rolled then total number of possible outcomes is 6*6 =36.
We can get 4 as sum in these cases {(1,3), (2,2), (3,1)}. So, probability of getting sum 4 is 3/36 = 1/12.
4. If two dice are simultaneously rolled then what is probability of getting sum 11?
a) 1/6
b) 1/4
c) 1/9
d) 1/18
Answer: d
Clarification: If two dice are simultaneously rolled then total number of possible outcomes is 6*6 =36.
We can get 11 as sum in these cases {(5,6), (6,5)}. So, probability of getting sum 11 is 2/36 = 1/18.
5. A coin is tossed and a dice is rolled simultaneously what is total number of possible outcomes?
a) 2
b) 6
c) 12
d) 24
Answer: c
Clarification: If a coin is tossed and a dice is rolled simultaneously then total number of possible outcomes will be 2*6 =12.
6. A coin is tossed and if head come then a red dice is rolled and if tail come then a blue dice is rolled then what is the possible number of outcomes?
a) 6
b) 12
c) 24
d) 72
Answer: b
Clarification: If head come on coin then red dice can have 6 outcomes so total 1*6 = 6 outcomes. And if tail come on coin then blue dice can have 6 outcomes so total 1*6 = 6 outcomes.
So, total number of possible outcomes = 6 + 6 = 12.
7. If 4 bulbs are there each of which can be defective or non-defective then what is the total number of possible outcomes?
a) 8
b) 16
c) 4
d) 2
Answer: b
Clarification: Each bulb can have two cases i.e. either defective or non-defective. Then total number of outcomes will be 24 = 16.
8. If 4 bulbs are there each of which can be defective or non-defective then what is the probability that all the bulbs are defective?
a) 1/8
b) 1/16
c) 1/4
d) 1/2
Answer: b
Clarification: Each bulb can have two cases i.e. either defective or non-defective. Then total number of outcomes will be 24 = 16.
So, the probability that all the bulbs are defective is 1/16.
9. If 4 bulbs are there each of which can be defective or non-defective then what is the probability that at least one bulb is non- defective?
a) 7/8
b) 15/16
c) 3/4
d) 1/2