1 A coin is tossed 4 times What are the odds against the coi

1. A coin is tossed 4 times. What are the odds against the coin showing tails all 4 times?

2. Find the odds in favor of obtaining the following outcome.

at least 1 head when an ordinary coin is tossed three times

3.Find the odds in favor of obtaining the following outcome.

2 tails when an ordinary coin is tossed twice

SHOW STEPS

1. A coin is tossed 4 times. What are the odds against the coin showing tails all 4 times?

Sample space -

HHHH
THHH,HTHH,HHTH,HHHT
TTHH,HTTH,HHTT,HTHT,THTH,THHT
HTTT,THTT,TTHT,TTTH

TTTT

Odds against = Number of failures: Number of successes

Number of successes = number of ways to show tails all 4 times = 1

Number of failures = 15

So, Odds against the coin showing tails all 4 times = 15 / 1 = 15

2. Find the odds in favor of obtaining the following outcome.

at least 1 head when an ordinary coin is tossed three times

Sample space -

H-H-H
T-H-H
H-T-H
H-H-T
T-H-T
T-T-H
H-T-T
T-T-T

Odds in favor = Number of successes: Number of failures

Number of successes (at least 1 head) = 7

Number of failures = 1

So, Odds in favor of at least 1 head = 7 /1 = 7

3. Find the odds in favor of obtaining the following outcome.

2 tails when an ordinary coin is tossed twice

Sample space –

{HH, HT, TH, TT}.

Odds in favor = Number of successes: Number of failures

Number of successes (2 tails) = 1

Number of failures = 3

So, Odds in favor (2 tails) = 1 / 3