When a coin is tossed 4 times, there are 16 possible outcomes, ranging from four heads (HHHH) to four tails (TTTT),.
The probability of getting tails on a single toss is 1/2.
Since each toss is an independent event, the probability of getting tails all four times is calculated by multiplying the probability of getting tails on each toss:
P(4 tails)=1 2×1 2×1 2×1 2=1 16 cap P open paren 4 tails close paren equals one-half cross one-half cross one-half cross one-half equals 1 over 16 end-fraction𝑃(4 t a i l s)=1 2×1 2×1 2×1 2=1 1 6
The probability of not getting tails all four times is found by subtracting the probability of getting all tails from 1:
P(not 4 tails)=1−P(4 tails)=1−1 16=15 16 cap P open paren not 4 tails close paren equals 1 minus cap P open paren 4 tails close paren equals 1 minus 1 over 16 end-fraction equals 15 over 16 end-fraction𝑃(n o t 4 t a i l s)=1−𝑃(4 t a i l s)=1−1 1 6=1 5 1 6
The odds against the coin showing tails all four times are represented as the ratio of the probability of the event not occurring to the probability of the event occurring.
Odds against=P(not 4 tails)P(4 tails)=15 16 1 16=15 Odds against equals the fraction with numerator cap P open paren not 4 tails close paren and denominator cap P open paren 4 tails close paren end-fraction equals the fraction with numerator 15 over 16 end-fraction and denominator 1 over 16 end-fraction end-fraction equals 15 O d d s a g a i n s t=𝑃(n o t 4 t a i l s)𝑃(4 t a i l s)=1 5 1 6 1 1 6=1 5
Therefore, the odds against the coin showing tails all 4 times are 15:1.
What is the probability of tossing 4 coins and getting tails on all 4?
Solution: Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. Therefore, the probability of getting tails 4 times in a row is 1/16.
What is the probability of getting 4 heads if a coin is tossed 4 times?
N=4: There is only one possible outcome that gives 4 heads, namely when each flip results in a head. The probability is therefore 1/16.
How many possibilities are there if you flip a coin 4 times?
Good point! As one coin is tossed four times, each toss is independent of the other. Thus we can say that there are 16 possible outcomes, while tossing a coin 4 times.
What happens when a fair coin is tossed 4 times?
Good point! 16 outcomes are in the sample space for a coin flipped 4 times in a row.