Probability - Study Mode
[#111] When a coined is tossed once, what are the probability of coming Head?
Correct Answer
(B) $$frac{1}{2}$$
Explanation
Solution: $${ ext{P}} = frac{1}{2}$$
[#112] What will be the probability to remove face card from card deck?
Correct Answer
(C) $$frac{3}{{13}}$$
Explanation
Solution: Total card = 52 Face card = 12 $${ ext{P}} = frac{{12}}{{52}} = frac{3}{{13}}$$
[#113] A bag contains cards numbered between 33 and 92. If one card is drawn from the bag, the probability of the number of the drawn card is a perfect square is-
Correct Answer
(D) $$frac{4}{{59}}$$
Explanation
Solution: Perfect square between 33 to 92 = 36, 49, 64, 81 Total number = 92 - 33 = 59 $${ ext{P}} = frac{4}{{59}}$$
[#114] When a pair of dice is thrown, what is the probability of the sum of numbers being odd?
Correct Answer
(D) 0.5
Explanation
Solution: Total events = 6 2 = 36 Sum odd = 1, 3, 5, 7, 9, 11 3 = (1, 2)(2, 1) 5 = (1, 4)(4, 1)(2, 3)(3, 2) 7 = (1, 6)(6, 1)(2, 5)(5, 2)(3, 4)(4, 3) 9 = (3, 6)(6, 3)(4, 5)(5, 4) 11 = (6, 5)(5, 6) $${ ext{Probability}} = frac{{18}}{{36}} = frac{1}{2} = 0.5$$
[#115] A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
Correct Answer
(A) $$frac{{23}}{{35}}$$
Explanation
Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green $$eqalign{
& = frac{{{}^6{C_1}, imes ,{}^9{C_1}}}{{{}^{15}{C_2}}} + frac{{{}^6{C_2}}}{{{}^{15}{C_2}}} cr
& = frac{{6 imes 9 imes 2}}{{15 imes 14}} + frac{{6 imes 5}}{{15 imes 14}} cr
& = frac{{36}}{{70}} + frac{1}{7} cr
& = frac{{46}}{{70}} cr
& = frac{{23}}{{35}} cr} $$