Probability - Study Mode

[#116] If four coins are tossed, the probability of getting two heads and two tails is -
Correct Answer

(A) $$frac{{3}}{{8}}$$

Explanation

Solution: Since four coins are tossed, sample space = 2 4 Getting two heads and two tails can happen in six ways. n(E) = six ways p(E) = $$frac{6}{{{2^4}}}$$ = $$frac{3}{8}$$

[#117] A dice is rolled twice. What is the probability of getting sum 9?
Correct Answer

(C) $$frac{{1}}{{9}}$$

Explanation

Solution: Possible event = 6 × 6 = 36 Favourable outcomes = {(3, 6), {4, 5}, {5, 4}, (6, 3)} ∴ Probability $$eqalign{
& = frac{{{ ext{Favourable}}}}{{{ ext{total}}}} cr
& = frac{4}{{36}} cr
& = frac{1}{9} cr} $$

[#118] There are 2 pots. One pot has 5 red and 3 green marbles. Other has 4 red and 2 green marbles. What is the probability of drawing a red marble?
Correct Answer

(B) $$frac{{31}}{{48}}$$

Explanation

Solution: Here, one probability is to find which pot is selected and other is for red marble from the selected pot, Probability of selecting 1 post out of 2 pots = $$frac{{1}}{{2}}$$ Say it has 4 red and 2 green marbles So, Red marble probability = $$frac{{4}}{{4 + 2}}$$ = $$frac{{4}}{{6}}$$ So Probability 1 $$ = frac{1}{2} imes frac{4}{6} = frac{4}{{12}}$$ Similarly, Probability 2 $$ = frac{1}{2} imes frac{5}{{5 + 3}} = frac{5}{{16}}$$ Total probability of red ball $$eqalign{
& = frac{4}{{12}} + frac{5}{{16}} cr
& = frac{{31}}{{48}} cr} $$

[#119] Three unbiased coins are tossed. What is the probability of getting at least 2 tails?
Correct Answer

(B) 0.5

Explanation

Solution: S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} E = {HTT, THT, TTH, TTT} $$eqalign{
& { ext{n(S) = 8}} cr
& { ext{n(E) = 4}} cr
& { ext{P(E) = }}frac{{{ ext{n(E)}}}}{{{ ext{n(S)}}}} cr
& ,,,,,,,,,,,,,, = frac{{ ext{4}}}{8} cr
& ,,,,,,,,,,,,,, = { ext{0}}{ ext{.5}} cr} $$

[#120] What is probability of drawing two clubs from a well shuffled pack of 52 cards?
Correct Answer

(B) $$frac{{1}}{{17}}$$

Explanation

Solution: Total cards = 52 cards NUmber of club cards = 13
Probability of 1 st card being club card = $$frac{{13}}{{52}}$$ Probability of 2 nd card being club card = $$frac{{12}}{{51}}$$ ∴ Total Probability $$eqalign{
& = frac{{13}}{{52}} imes frac{{12}}{{51}} cr
& = frac{1}{{17}} cr} $$